Just a thought...
If you are a proton flying through the accelerator complex, you see the world around you malformed by Lorentz contraction. This gives some interesting relativistic weirdness. Also, the time perception of the proton changes.
(The computations below are based on the fact that a proton's rest mass is almost exactly 1GeV, and that the energy is conveniently proportional to the Lorentz contraction.)

Linac 2: energy goes up to 50 MeV, so the end of the accelerator appears about 5 % shortened to a proton.

PSB: energy goes up to 1.4 GeV. This means that at injection, the ring appears 25 m long, shrinking to 18 m.

PS: energy goes up to 25 GeV, so the 628 m long ring shrinks from about 450 m to 25 m.

SPS: energy goes up to 450 GeV, so the 6.9 km long ring shrinks from about 280 m to 15 m.

LHC: finally, the proton enters the 26.6 km long ring that appears to shrink from 59 m to 4 m.

So, for a proton, the whole accelerator complex consists of shrinking rings of about equal size, where the LHC is shortest. Also, the proton stays in the LHC for a few seconds before dumping: 10 hours becomes 5 seconds.

Even weirder - while the proton can consider its path around the main ring only 4 m long, it does not see the ring shrunk to 4 m circumference. The component of the ring size perpendicular to the proton's immediate motion is not contracted, so the ring appears squished to an oval about 2m deep and 8.5 km wide with the proton at the end and it rolls around the proton like a crazy rotating converor belt.